mc::estimators::MCMeanEstimator< dim > Class Template Reference

Uniform Monte Carlo mean estimator. More...

#include <MCMeanEstimator.hpp>

Collaboration diagram for mc::estimators::MCMeanEstimator< dim >:

Public Member Functions
MeanEstimate< dim >	estimate (const mc::domains::IntegrationDomain< dim > &domain, std::uint32_t seed, std::size_t n_samples, const std::function< double(const mc::geom::Point< dim > &)> &f) const
	Estimate the mean of a function over a domain using uniform sampling.

Detailed Description

template<std::size_t dim>
class mc::estimators::MCMeanEstimator< dim >

Uniform Monte Carlo mean estimator.

Template Parameters

dim	Dimensionality of the space.

Estimates the mean of f over domain Ω by:

1. Sampling N points uniformly in bounding box
2. Filtering to points inside Ω: x₁, ..., x_M where M ≤ N
3. Computing μ̂ = (1/N) ∑ᵢ f(xᵢ) · 𝟙[xᵢ ∈ Ω]
4. Estimating variance: σ̂² = E[f²] - μ̂²
5. Standard error: SE = σ̂/√N

The mean (before multiplying by volume) is the empirical average over all N trials (treating out-of-domain points as contributing 0).

Note

Uses parallel sampling with OpenMP for efficiency.

Definition at line 57 of file MCMeanEstimator.hpp.

Member Function Documentation

estimate()

template<std::size_t dim>

MeanEstimate< dim > mc::estimators::MCMeanEstimator< dim >::estimate	(	const mc::domains::IntegrationDomain< dim > &	domain,
		std::uint32_t	seed,
		std::size_t	n_samples,
		const std::function< double(const mc::geom::Point< dim > &)> &	f
	)		const

Estimate the mean of a function over a domain using uniform sampling.

Parameters

domain	The integration domain.
seed	Random seed for reproducibility.
n_samples	Total number of sample points to generate.
f	Function to evaluate (only at points inside domain).

Returns

MeanEstimate with mean, stderr, and sample counts.

Exceptions

std::invalid_argument

if n_samples == 0.

Parallel sampling: each thread gets a deterministic RNG stream and samples its portion of n_samples uniformly in the domain's bounding box. Only points inside the domain contribute to the sum.

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The documentation for this class was generated from the following file:

• src/montecarlo/estimators/MCMeanEstimator.hpp